Question

solve for q and graph the solution. -2q - 3 > -3 or $\frac{q + 11}{4}>4$. plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first - inequality

Solve $-2q - 3>-3$. Add 3 to both sides: $-2q-3 + 3>-3 + 3$, which simplifies to $-2q>0$. Divide both sides by - 2 and reverse the inequality sign (since dividing by a negative number), we get $q < 0$.

Step2: Solve the second - inequality

Solve $\frac{q + 11}{4}>4$. Multiply both sides by 4: $q + 11>16$. Subtract 11 from both sides: $q+11 - 11>16 - 11$, so $q>5$.

Step3: Graph the solution

For $q < 0$, the endpoint is 0 and it is an open - circle (because the inequality is $<$) and the line goes to the left. For $q>5$, the endpoint is 5 and it is an open - circle (because the inequality is $>$) and the line goes to the right.

Answer:

The solution of the compound inequality is $q < 0$ or $q>5$. On the number - line, there is an open - circle at $q = 0$ with a line extending to the left and an open - circle at $q = 5$ with a line extending to the right.